Multiprocessor Synchronization Algorithms (20225241) Lecturer: Danny Hendler

Electronic submissions only!!! Grade structure 3 (theoretic) problem sets Up to 30% of grade Take-home final exam At least 70% of grade Electronic submissions only!!!

Adminstrative details Office: Alon 218 Office hours: Mondays, 2pm-4pm Or make an appointment Course site: http://www.cs.bgu.ac.il/academics/courses/2009/a/220225401 (or simply enter through my home page)

Books Distributed Computing: Fundamentals, Simulations, and Advanced Topics, Hagit Attiya and Jennifer Welch, John Wiley and Sons Synchronization Algorithms and Concurrent Programming, Gadi Taubenfeld, Pearson/Prentice Hall. Book site: http://www.faculty.idc.ac.il/gadi/book.htm

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Moore’s law Exponential growth in computing power 6

How can we write correct and efficient algorithms for multiprocessors? The Future of Computing Speeding up uni-processors is harder and harder Intel, Sun, AMD, IBM now focusing on “multi- core” architectures Soon, most computers will be multiprocessors How can we write correct and efficient algorithms for multiprocessors? 7

Distributed Systems The Internet A distributed system is a collection of individual computing devices that communicate with one another. E.g.: VLSI chips Shared-memory multiprocessor Local-area network The Internet

One sequential model, MANY distributed models Shared-memory / Message-passing Which operations are allowed (read, write, read-modify-write)? Synchronous, timing-conditions, asynchronous Are failures allowed? Fail-stop, Byzantine failures, message omission Is the number of processes known?

Types of distributed systems Multi-core computers The Internet Peer-to-peer systems Grid computers Wireless networks Sensor networks Ad-hoc networks …

Motivating examples of Synchronization

The Too-Much-Milk Problem Time Alice Bob 5:00 Arrive Home 5:05 Look in fridge; no milk 5:10 Leave for grocery 5:15 Arrive home 5:20 Arrive at grocery 5:25 Buy milk 5:30 Arrive home; put milk in fridge 5:40 5:45 Arrive home; too much milk! Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

Solving the Too-Much-Milk Problem Required properties Mutual Exclusion: Only one person buys milk “at a time” Progress: Someone always buys milk if it is needed Communication primitives Leave a note (set a flag) Remove a note (reset a flag) Read a note (test the flag) Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

Important Distinction Safety Property Nothing bad ever happens Example: mutual exclusion Liveness Property Something good happens eventually Example: progress Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

Solution 1 Alice if (no milk) { if (no note) { leave Note buy milk remove note } Bob Does it work? No, may end up with “two milk”. mutual exclusion progress Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

Solution 2 Using labeled notes Alice leave note A if (no note B) { if (no milk) {buy milk} } remove note A Bob leave note B if (no note A) { remove note B No, may end up with no milk. mutual exclusion progress Does it work? Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

Solution 3 Alice leave note A while (note B) {skip} if (no milk) {buy milk} remove note A Bob leave note B if (no note A) { } remove note B Does it work? mutual exclusion progress Only if we make a timing assumption! Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

Solution 4 Using 4 labeled notes A1 A2 B2 B1 the fridge’s door Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

Solution 4 A correct, fair, symmetric algorithm! Alice leave A1 if B2 {leave A2} else {remove A2} while B1 and ((A2 and B2) or (no A2 and no B2)) {skip} if (no milk) {buy milk} remove A1 Bob leave B1 if (no A2) {leave B2} else {remove B2} while A1 and ((A2 and no B2) or (no A2 and B2)) remove B1 A correct, fair, symmetric algorithm! Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

Solution 4 A1 A2 X B2 X B2 A1 A2 B2 B1 A1 A2 B2 B1 Alice’s turn These should be interpreted as follows: if the participant (Alice/Bob) evaluates the waiting condition and finds out that the condition depicted in the box is met – it can safely buy milk if there is none. Bob’s turn Bob’s turn Bob’s turn Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

A variant of Solution 4 The order of the first two statements is replaced Is it correct ? Alice if B2 {leave A2} else {remove A2} leave A1 while B1 and ((A2 and B2) or (no A2 and no B2)) {skip} if (no milk) {buy milk} remove A1 Bob if (no A2) {leave B2} else {remove B2} leave B1 while A1 and ((A2 and no B2) or (no A2 and B2)) remove B1 No, may end up with two milk. B2 A1 B2 B2 B2 B2 B1 Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

A variant of Solution 4 The order of the first two statements is replaced Is it correct ? Alice if B2 {leave A2} else {remove A2} leave A1 while B1 and ((A2 and B2) or (no A2 and no B2)) {skip} if (no milk) {buy milk} remove A1 Bob if (no A2) {leave B2} else {remove B2} leave B1 while A1 and ((A2 and no B2) or (no A2 and B2)) remove B1 MILK No, may end up with two milk. B2 A1 B2 B2 B2 B1 B2 mutual exclusion progress Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

The coordinated attack problem Blue army wins if both blue camps attack simultaneously Design an algorithm to ensure that both blue camps attack simultaneously Enemy 1 2 The problem is due to by Jim Gray (1977) Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

The coordinated attack problem Communication is done by sending messengers across valley Messengers may be lost or captured by the enemy  Enemy 1 2 Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

The coordinated attack problem Theorem: There is no algorithm that solves this problem ! Proof: Assume to the contrary that such an algorithm exits. Let P be an algorithm that solves it with the fewest # of messages, when no message is lost. P should work even when the last messenger is captured. So P should work even if the last messenger is never sent. But this is a new algorithm with one less message. A contradiction.  The model is too weak! Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006